REGULAR ARTICLE
Transfer of multivariate calibration model for simultaneous electrochemical determination of ascorbic acid and uric acid
YASAMAN SEFID-SEFIDEHKHAN, HANEIE SALEHNIYA, MARYAM KHOSHKAM* and MANDANA AMIRI
Department of Chemistry, Faculty of Science, University of Mohaghegh Ardabili, 56199-11367 Ardabil, Iran E-mail: khoshkam@uma.ac.ir
MS received 12 May 2021; revised 10 July 2021; accepted 12 July 2021
Abstract. Multivariate analysis is one of the most interesting analytical methods in the analysis of many electrochemical data from pharmaceutical and biological analytes. However, there are some challenges in the electrochemical analysis including potential shifts from sample to sample and alterations in the baselines. To minimise the effect of these alterations in baselines and potentials, one tries to do all experiments in one day.
However, this is impossible when there are many samples. Calibration transfer is one of the most interesting methods to transfer calibration model between two conditions or two instruments. In this study, a calibration transfer strategy was used to transfer the multivariate calibration model of DPV data from a mixture of ascorbic acid (AA) and uric acid (UA) in the same experimental condition but two different times. The data were recorded from the unmodified electrode and the voltammetric peaks of target compounds are overlapped with each other, making it impossible to be estimated by conventional univariate electrochemical methods. In this study, it was shown that before calibration transfer the prediction results are not accurate and the per cent of relative error in predicted concentration from slave data was comparable to the per cent of relative error in a predicted concentration of UA and AA in the master data.
Keywords. DWPDS; Differential pulse voltammetry; Calibration transfer; Ascorbic acid; Uric acid.
1. Introduction
During the past four decades, Chemometrics methods have been used for the analysis of electrochemical data.1Chemometrics methods have been used to solve the systems with high overlap signals. There is a big challenge in the analysis of electrochemical data which is the non-linearity of electrochemical data that leads to limited utilization of chemometrics methods in electroanalytical chemistry.2 This problem is seen as the potential shift in electrochemical data.3Several strategies have been used for the calibration of non- linear data systems such as: data pretreatment, the use of linear methods, the use of local modelling, the addition of extra variables, the use of non-linear cali- bration techniques.4
Another important limitation in electrochemical data is the fact that for the same solutions and exper- imental conditions, there is a difference between
signals when the signals are recorded at different times. These differences can be caused by instrument characteristics, detector characteristics, and type of sample presentation. Consequently, correcting these differences is necessary and can be achieved (1) by constructing new calibration models on each new determination or (2) by performing calibration transfer in order to reuse the initially developed models.5
Calibration transfer is a procedure of data transfor- mation that allows reuse of the calibration model from the main condition or instrument (primary or master) for prediction of data obtained in secondary or slave or secondary conditions and permit accurate analysis of data without the need for a recalibration of data in slave or secondary condition.6
Calibration transfer may provide a good balance on analytical accuracy and cost. Different approaches are proposed for calibration transfer including Direct Standardization (DS), Piecewise Direct
*For correspondence
Supplementary Information: The online version contains supplementary material available athttps://doi.org/10.1007/s12039-021- 01982-7.
https://doi.org/10.1007/s12039-021-01982-7Sadhana(0123456789().,-volV)FT3](0123456789().,-volV)
Standardization (PDS),7 double window Piecewise Direct Standardization (DWPDS),8–10 Orthogonal signal correction (OSC),11,12 slope and bias correction (SBC),7 finite impulse transform (FIR)13 and wavelet transform (WT);14 In some of these methods per- forming calibration transfer needs a selection of a set of samples from the master calibration and remeasure them on the secondary situation. So far, this strategy has been widely used in combination with electro- chemical,15,16 Raman,17,18 near-infrared (NIR),19 nuclear magnetic resonance (NMR).20 There are, several studies that have been used multivariate cali- bration and calibration transfer methods together.16,21 Due to the urgent need for adaptability of mea- surements with different devices and even the same devices at different times, the industry pays special attention to aspects related to different calibration transfer methods.
Ascorbic acid (AA) is a soluble vitamin that is usually present in many biological systems and mul- tivitamin formulations. It is broadly utilized to provide a sufficient dietary intake and also as an antioxidant.
Its inordinate dose may cause headache, trouble sleeping, gastrointestinal discomfort and flushing of the skin.22 Ascorbic acid has been used for the pre- vention and treatment of common colds, mental ill- nesses, infertility, cancers, and some clinical manifestations of HIV infections.23 Uric acid (UA) is the main product of purine metabolism. UA is a key biomolecule found in urine and blood. Constant monitoring of UA in the body fluid is needed since its abnormal concentration levels lead to various diseases, such as hyperuricemia, gout, leukemia, pneumonia and LeschNyhan syndrome.24 Scheme 1 shows the struc- ture of AA and UA, respectively. The simultaneous detection of ascorbic acid (AA) and uric acid (UA) in a biological sample has gained substantial attention because they exist together in a living system and play crucial roles in physiological functions and diagnosing diseases.25 Several analytical methods for individual or simultaneous determination of AA and UA have been reported in the literatures such as RP-HPLC,26,27 spectrophotometry,28,29 spectroscopy30,31 and capil- lary zone electrophoresis.32,33 The problem is that
these methods can be expensive and need complex procedures.
Owing to the redox properties of AA and UA, the electrochemical techniques have focused attention because its low cost, simple operation and rapid response.34
Yet, in synchronous electrochemical detection of UA and AA, overlapped electrochemical signals are achieved. To solve this problem, the most widely used method is differential pulse voltammetry (DPV) with modified electrodes. This technique provides low detection limits and good peaks resolution. These facts have motivated the development of a lot of modified electrodes for the simultaneous determination of these biomolecules with modifiers,35 some of them are:
Carbon nanotube,36,37 gold nanoparticle,38 silver nanoparticle,39 graphene oxide40 and so on.
The used chemometric techniques to the simulated determination of AA and UA are: normalized root mean square error (NRMSE),22 artificial neural net- works (ANN),41 fractional factorial and Doehlert design,42 APARAFAC and MCR-ALS,43 COW, AsLS, U-PLS44 partial least squares-1 (PLS-1), con- tinuum power regression (CPR), multiple linear regression-successive projections algorithm (MLR- SPA), robust continuum regression (RCR), partial robust M-regression (PRM), polynomial-PLS (PLY- PLS), spline-PLS (SPL-PLS), radial basis function- PLS (RBF-PLS), least squares-support vector machi- nes (LS-SVM), wavelet transform-artificial neural network (WT-ANN), discrete wavelet transform-ANN (DWT-ANN) and back propagation-ANN (BP-ANN).4 Moreover, we did not find electrochemical methodologies described for the simultaneous deter- mination of ascorbic acid and uric acid with an unmodified electrode. An attractive way to solve the problem of overlapped signals is the use of electro- chemistry techniques combined with chemometrics methods.
In this work, we use DPV for simultaneous deter- mination of AA and UA with an unmodified electrode.
The main points in this study are (1) the electrode is unmodified and thus the peaks are overlapped and (2) the DPV of calibration data and prediction data were recorded at different times and there is a shift in the potential of the calibration set and prediction set.
These alterations in data was corrected by DWPDS method without any further data pretreatment method.
To our knowledge, the applied method is the first application of calibration transfer to correct the dif- ferences in DPV of the same samples recorded in different times and reusing the old calibration model for prediction of new samples.
Scheme 1. Chemical structure of (a) Ascorbic acid, (b) Uric acid.
1.1 Calibration transfer
Totally calibration transfer relates the response of a calibration sample in master or primary condition 1 (X1) to the response obtained in secondary or slave or secondary condition (X2), by calculation of transfor- mation matrix F, according to the equation:
X2¼X1F ð1Þ
In our study, master or primary condition corre- sponds to DPV signals recorded on the first day (experiment 1) and slave or secondary condition is for DPV signals measured one month later (experi- ment 2). Different methods of calibration transfer are different in the way of calculation of transformation matrix.
1.1a PDS and DWPDS: DWPDS is a modified ver- sion of PDS. Thus first we explain the algorithm of PDS briefly. More explanations of this method can be found elsewhere.7
In PDS, the transformation matrix is calculated based on regression between ith wavelengths of master data to the corresponding wavelengths contained in a moving window (fromi-k toi?k) on the slave data.
The regression vectors calculated for each window in the data are then assembled to form a banded diagonal matrix F, according to
F¼diagðb1;b2; . . .;bi; . . .;bkÞ ð2Þ
where k is the number of channels.
The response (xs) of sample from slave condition can then be transferred to master or primary condition using the transfer matrixF according to
xs!m¼xsF ð3Þ
where xs?m represents the transformed data of prediction sample in slave or secondary condition after applying for calibration transfer and xs is original data of prediction sample in slave or sec- ondary condition before calibration transfer. PDS models is a good method where features are present in the transfer spectra, but in the case of featureless regions is not a good method.10 Thus, a further modification has been made on PDS algorithm applying a double window (DWPDS),8 DWPDS is based on assuming two windows on both primary and secondary conditions during calibration trans- fer, which increases the modelling flexibility. The base of this method is identical to PDS and some authors have considered it as the best method in transferring the NIR data.9
2. Experimental
2.1 Chemical reagents
Phosphate and acetate buffer solutions (0.1M) were prepared and used as a supporting electrolyte in pH range of (2.0, 3.0, 6.0, 7.0, using KH2PO4and H3PO4) and (pH=4,5, using Sodium Acetate Solution) respectively. Stock solutions of AA and UA were freshly prepared in an appropriate buffer solution. All chemicals were analytical reagent grade from Merck.
All aqueous solutions were prepared with doubly distilled deionized water.
2.2 (Instrumentation) apparatus
Voltammetric experiments were performed by using a Metrohm Computrace voltammetric analyzer model 797VA. A conventional three-electrode system was applied with a carbon paste electrode (CPE) as a working electrode, a KCl-saturated Calomel reference electrode and a Pt wire as the counter electrode. A digital pH/mV/Ion meter was used for the preparation of the buffer solutions, which were used as the sup- porting electrolyte in the voltammetric experiments.
Voltammetric data were analyzed in the Matlab 2013 environment and the PLS Toolbox 4.1.1 from Eigen- vector Inc.
2.3 Preparation of carbon paste electrode
By mixing graphite powder with an appropriate amount of mineral oil (Nujol) by using a mortar and pestle (75:25, w/w), the CPE was prepared. A small portion of the composite mixture was packed into the end of a Teflon tube (about 3.0 mm i.d.). Electrical contact was made by forcing a copper pin down into the Teflon and into the back of the composite. Bare electrode was polished on paper in order to obtain a smooth and shiny surface.
3. Results and Discussion
3.1 Electrochemical behavior of UA and AA
Cyclic voltammetry (CV) and Differential pulse voltammetry (DPV) were employed for investigation and determination of electrochemical behavior of UA and AA. Figure1shows the cyclic voltammograms for UA and AA at the CPE. UA and AA peaks appear at 0.353 V and 0.301 V, respectively, in PBS (pH 6.0).
No reduction peak was observed in the cyclic voltammograms of AA and UA. The peak potentials difference of about 0.051 V between both oxidation peaks clearly shows the simultaneous determination of AA and UA at CPE is not possible, spatially in low concentration.
3.2 The effect of pH on electrochemical response of AA and UA
The influence of pH on the oxidation peak potentials and currents of 1.0 mM AA and UA was studied in 0.1 M phosphate buffer solutions (PBS) with different pHs (2, 3, 6 and 7), as well as 0.1 M acetate buffer solutions with pHs equal to 4 and 5, as shown in Figure S1 (a), Supplementary Information. The results exhibited that with the increase in pH, the anodic peak potentials (Epa) for both species, shifted towards more negative values, which illustrates the involvement of hydrogen ions in the electro-oxidation of AA and UA.
The relationships between the peak potentials and pH lead to the following linear regression equations:
(shown in Figure S1(b), SI)
Ep Vð Þ ¼ 0:5370:041pH R2¼0:900 for AA Ep Vð Þ ¼ 0:7250:060pH R2¼0:996
for UA It can be concluded that number of electrons transferred is equal to protons in case of UA.
The maximum oxidation peak current was observed at a pH of 6.0 for UA analysis. It was selected as the optimum pH for the determination of both drugs.
3.3 The effects of scan rate
The scan rate is one of the most important factors that affect the behavior of the electrochemical mechanism and kinetics of electron transfer of drugs. In order to investigate the effect of scan rate on the cyclic voltammograms of AA and UA, the responses of the CPE to UA and AA were recorded in the PBS (0.1 M, pH 6) in different scan rates (20 to 200 mV s-1) and the results are shown in Figure S2 (a) and S2 (c), respectively. As can be seen, the oxidation peak cur- rent shows a linear relation to the square root of the scan rate (t), with the following linear equation (Figure S2 (b) and (d)):
Ipað Þ ¼lA 4:963t1=2mVs11=2
þ4:657 R2¼ 0:992
for AA
Ipað Þ ¼lA 10:01t1=2mVs11=2
2:291 R2¼ 0:989
for UA
The results indicated that the oxidation of UA and AA on the surface of the CPE was followed by a diffusion-controlled mechanism. Additionally, the EP of AA and UA shifted positively as increasingtwhich confirmed that the electrode reaction was irreversible.
In this study, 100 mVs-1 was chosen as the optimum scan rate because at this value, the sensitivity was relatively high and the voltammetric curves were well- shaped with a relatively narrow peak width.
3.4 Univariate calibration of a single component (AA and UA)and limit of detection
Differential pulse voltammetry (DPV) was applied as a highly sensitive and rapid electrochemical method for the detection of trace amounts of UA and AA.
Figure2a exhibits DPVs for buffered solutions of UA at pH 6.0. A dynamic linear range in the concentration range of 1.0910-6–5.0910-3mol L-1and detection limit of 1.9910-7 M was obtained. The linear equa- tions for the first linear range is Ip/lA= 7.275?
(164.2C) (R2 = 0.9923, C is in mM) (see Figure2b).
Figure2c exhibits DPVs for buffered solutions of AA at pH 6.0. A dynamic linear range in the concentration range of 1.0 9 10-3–1.0 9 10-5 M and a detection limit of 4.33910-6 M were obtained. The linear equations for the first range is Ip/lA= -0.096? (30.97C) (R2= 0.999, C is in mM) (see Figure 2d)
-10 10 30 50 70 90
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
AA UA UA+AA
Figure 1. Cyclic voltammograms of 0.1 mM UA at the surface of CPE (red line), 0.1 mM AA (blue line) and 0.1 mM mixture of UA and AA (green line), in 0.1 M PBS, pH 6.0. Sweep rate was 100 mV s-1.
3.5 Simultaneous determination of UA and AA in a mixture
3.5a Calibration and prediction on the master or primary condition: Figures 3a and 3b show the
DPVs of the AA and UA mixture. These two voltammograms are for identical samples which are different only in the time of their measurement. It is clear that univariate calibration of this data is impos- sible due to the high overlap of oxidation peaks on the Figure 2. (a) Differential pulse voltammograms (50 mV pulse amplitude, 5 mV step potential) for the oxidation of UA in phosphate buffer solution pH 6.0 at CPE (Up to down: 1.0910-3, 5.0910-3, 1.0910-4, 5.0910-4, 1.0910-5, 5.09 10-5, 1 910-6M), (b) plot of the peak current in differential pulse voltammetry versus the UA concentration (1.0 9 10-3M to 1.0910-6 M). (c) Differential pulse voltammograms (50 mV pulse amplitude, 5 mV step potential) for the oxidation of AA in phosphate buffer solution pH 6.0 at CPE (Up to down: 1.0910-3, 5.0910-3, 1.0910-4, 5.0910-4, 1.0910-5M), (d) plot of the peak current in differential pulse voltammetry versus the AA concentration (1.0910-3M to 1.0910-5M).
Figure 3. (a) DPV of a mixture of UA and AA in master or primary condition in PBS 0.1 M, pH= 6 and scan rate 100 mVs-1, the concentration of UA and AA were according to the last two columns in table1. (b) DPV of a mixture of UA and AA in slave or secondary condition, similar to master or primary condition and identical samples one month later (c) difference of master and slave spectra (d) comparison of a:master spectra of sample 7, b: slave spectra of sample 7 before calibration transfer and c: slave spectra of sample 7 after calibration transfer.
surface of the unmodified electrode. In the first step calibration model was built from PLS model and the prediction set in space of master or primary condition was predicted. The first two columns in Table 1Show the predicted concentrations and per cent of relative error in predicted concentrations of ten samples. As can be seen in this table, %RE were 5.56% and 5.55%
for AA and UA, respectively. It should be noticed that in this case DPV of calibration and prediction samples were recorded in one day.
3.5b Calibration on master and prediction on slave before calibration transfer: In this section calibra- tion model was built based on data obtained in
master or primary condition and this model was used for the prediction of slave data. The two columns in the second column in Table1(condition 2) show that the predicted concentrations are not accurate and
%RE is very high in this case (67.72% and 56.89%
for AA and UA, respectively). This is correct because as shown in Figure 3c, the DPV of the prediction samples in master or primary condition is quite dif- ferent from DPV of identical samples in master or primary condition. Thus it is reasonable that the built calibration model on master or primary condition is not suitable for the prediction of UA and AA con- centrations in slave data. In this case, DPV of Table 1. Predicted and real concentration of UA and AA after and before calibration transfer
Condition 1* Condition 2** Condition 3*** True concentration****
AA UA AA UA AA UA AA UA
Sample 1 2.09E-05 2.30E-04 -9.51E-05 3.14E-04 2.48E-05 2.26E-04 2.10E-05 2.18E-04 Sample 2 2.18E-05 6.83E-04 -1.05E-04 6.83E-04 2.42E-05 6.00E-04 2.10E-05 6.17E-04 Sample 3 2.20E-05 8.22E-04 -3.16E-04 8.61E-04 2.33E-05 8.63E-04 2.10E-05 8.17E-04 Sample 4 2.40E-04 1.89E-05 1.79E-04 -6.89E-06 2.51E-04 1.70E-04 2.27E-04 1.78E-05 Sample 5 2.79E-04 4.21E-04 -6.74E-06 5.34E-04 2.63E-04 4.10E-04 2.27E-04 4.17E-04 Sample 6 4.08E-04 2.77E-04 2.42E-04 2.02E-04 4.18E-04 2.19E-04 4.26E-04 2.18E-04 Sample 7 4.13E-04 6.43E-04 1.45E-04 8.00E-04 4.35E-04 6.12E-04 4.26E-04 6.17E-04 Sample 8 4.37E-04 7.99E-04 -2.52E-05 -8.19E-05 4.33E-04 8.19E-04 4.26E-04 8.17E-04 Sample 9 6.53E-04 4.21E-04 3.39E-04 6.46E-04 6.06E-04 4.24E-04 6.24E-04 4.17E-04 Sample 10 6.30E-04 6.14E-04 3.85E-04 7.63E-04 5.63E-04 6.24E-04 6.24E-04 6.17E-04
%RE***** 5.56 5.55 67.72 56.89 6.55 9.41 - -
*Condition 1: Calibration and prediction on the master or primary condition
**Condition 2: Calibration on master and prediction on the slave before calibration transfer
***Condition 3: Calibration on master and prediction on the slave after calibration transfer
****Condition 4: Real concentration
***** %RE=1009
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn
i¼1ðCiCbiÞ
Pn i¼1C2i
s
Figure 4. Schematic representation of an applied method in this study.
prediction samples were recorded one month later than DPV of calibration sample.
3.5c Calibration on master and prediction on the slave after calibration transfer: In this section first DWPDS calibration transfer was applied on slave data and then predicted with a built calibration model on master data. Figure4show the schematic presentation of the applied method in this study.
The results are shown in the third column of Table1 (condition 3). It is clear that the prediction error was reduced significantly and is comparable with obtained results in condition 1 in this table (6.55% and 9.41% for AA and UA, respectively). Figure 4shows the predic- tion spectra of sample 7 in (a) master or primary condition (b) in slave or secondary condition before calibration transfer and (c) in slave or secondary condition after calibration transfer. From this Figure, it is clear that the transferred DPV is very similar to the master or primary condition. These results confirmed that calibration transfer in this situation leads to accurate results. However in absence of calibration transfer as shown in Table1the results are not accurate.
4. Conclusions
In this work, an interesting application of multi-way calibration transfer was introduced to electroanalyt- ical data. First-order DPV data was recorded at two different times and PLS as a first-order calibration models was used for simultaneous determination of AA and UA. This study showed that calibration transfer can help to reuse a built calibration model from calibration data in master or primary condition for prediction of data in the same experimental condition which was recorded in another time. This method is an economic and time-saving method since it avoids the recalibration of data. It needs only a few calibration samples which should be acquired in slave or secondary conditions for calculation of transfer matrix. This study shows the potential of calibration transfer in the analysis of electrochemical data which suffer from a lack of repeatability with time. The applied method in this study not only is applicable in the transfer of signals from unmodified electrodes but also can be applied in the transfer of signals from modified electrodes.
Supplementary Information (SI)
Figures S1–S2 are available atwww.ias.ac.in/chemsci.
Acknowledgements
This study is a part of PhD project of Yasaman Sefide Sefideh khan and sponsored by the University of Moha- ghegh Ardabili (UMA) and the ministry of sciences, research and technology of Iran.
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